bpfig32.m

％ Atomizer Main Directory, Version .802 里面信号含有分解去噪合成过程的代码 ％---------------------------------------

% bpfig32: BP Figure 3.2 -- Analyzing FM-Cosine
%----------------------------------------------------------------------
% Signal:        FM-Cosine
%                s = .5*cos(n*pi*.5*t)
%                     + cos(n*pi*(t/2 + .5*cos(2*w*pi*t)/(4*w*pi)))
%                where w = 4
% Signal Length: 1024
% Dictionary:    Cosine Packets with D = log2(n)-4
% Observations:
%    (a) FM-Cosine.
%    (b) The ideal phase plane: a sinosoid plus a frequency modulated
%        oscillating cycles (four cycles).
%    (c) MOF plane gives a weak and smeared-out description of the FM
%        structure.
%    (d) BOB cannot resolve the nonorthogonality between the sinusoid
%        and the FM structure.
%    (e) MP cannot resolve the similarity among the 4 cycles in the
%        FM structure. It completely misses the FM structure.
%    (f) BP gives a good description of both the sinusoid and the
%        FM structure.
%
% Use:
%    bpfig32                   uses the current solver.
%    ATOMIZER_ENGINE = 1998;   selects original solver.
%    ATOMIZER_ENGINE = 2001;   selects later    solver.
%    Default is most recent solver.
%----------------------------------------------------------------------

%----------------------------------------------------------------------
%        1998: (S. Chen) Original script for BP paper.
% 09 Apr 2001: (M. Saunders) Choice of solvers implemented.
%----------------------------------------------------------------------

help bpfig32
bpengine;

n = 1024;   D = log2(n);   bell = 'Sine';   t = (1:n)' / n;
x = InputSignal('FM', n);

time  = cputime;
cMOF  = MOF(x, 'CP', D-4, bell, 0);
time1 = cputime - time;
time  = cputime;
cBOB  = BOB(x, 'CP', D-4, bell, 0);
time2 = cputime - time;
time  = cputime;
cMP   = MP(x, 'CP', D-4, bell, 0);
time3 = cputime - time;
time  = cputime;

switch ATOMIZER_ENGINE
  case 1998
    cBP = BP_Interior (x, 'CP', D-4, bell, 0);
 case 2001
    cBP = BP_Interior2(x, 'CP', D-4, bell, 0);
end
time4 = cputime - time;

fprintf('\n')
fprintf('CPU Running Time of MOF = %8.4e\n', time1);
fprintf('CPU Running Time of BOB = %8.4e\n', time2);
fprintf('CPU Running Time of  MP = %8.4e\n', time3);
fprintf('CPU Running Time of  BP = %8.4e\n', time4);

%--------------------
% Plots
%--------------------
fprintf('\nConstructing figure(%1g) ...\n', FIGURE)
figure(FIGURE);   clf reset;

subplot(3,2,1);   plot(t, x);
                  title('(a) Signal: FM');

subplot(3,2,2);   axis([0 1 0 1])
                  plot(t, .5*ones(1024, 1));
hold on

w   = 4; 
sig = cos(n * pi * (t/2 + .5 * cos(2*w * pi * t) / (4*w*pi)));
sig = sig + cos(n * pi * .5 * t) * .5;
tf  = 1/2 + .25 * sin(2 * w * pi * t);
plot(t, tf);      title('(b) Phase Plane: Ideal');
xlabel('Time');   ylabel('Frequency')

TFScale = 20;
subplot(3,2,6);   PhasePlane(cBP, 'CP', n, 0, 256, TFScale);
                  title('(f) PhasePlane: BP');
subplot(3,2,5);   PhasePlane(cMP, 'CP', n, 0, 256, TFScale); 
                  title('(e) PhasePlane: MP');
subplot(3,2,4);   PhasePlane(cBOB, 'CP',n, 0, 256, TFScale); 
                  title('(d) PhasePlane: BOB');
subplot(3,2,3);   PhasePlane(cMOF, 'CP',n, 0, 256, TFScale); 
                  title('(c) PhasePlane: MOF');